The 16-year-old Vekic advanced to the championship match with a 7-6 (7-5), 1-6, 6-3 decision over 16th-seeded 2009 Birmingham champion Magdalena Rybarikova at Edgbaston Priory Club.
It will be the second career finals appearance for Vekic, who also reached the Tashkent, Uzbekistan, title tilt last year, coincidentally also after downing Rybarikova in a semifinal.
Hantuchova, meanwhile, rallied for a 5-7, 6-1, 6-4 win over American qualifier Alison Riske.
The Slovakian veteran will be seeking her sixth career WTA Tour victory Sunday at the grass-court Wimbledon tuneup.
Swim Week Miami Beach 2014 [PHOTOS]